Signature verification is attracting increasing interest as a method for establishing the authority of a person to complete an automated transaction, gain control of a computer, gain physical entry to a restricted area, or the like. The person seeking permission to complete the transaction, etc., provides a sample of his signature, which is compared with a stored record. If the sample signature agrees sufficiently with the stored information, it is accepted as genuine.
In on-line methods of signature verification, the sample signature is made using digitizing apparatus, such as an instrumented tablet. The result is a digitized sample stream, which can be processed to extract characterizing information that can be stored compactly. One way to extract characterizing information is to compute functions, referred to as features, that map the sampled signature onto numerically valued single numbers or vectors. Thus, each sample signature is characterized by a corresponding set of feature values. During verification, these feature values are compared with stored, reference values of the same features, which have been computed on a reference set of signatures provided during an earlier registration procedure.
Broadly speaking, features fall into two categories: local features, and global features. Global features, such as total time and total length of the signature, are calculated for entire signatures or for substantial and distinct signature portions, such as contiguous pen-down portions. Local features are calculated for smaller portions, typically substantially smaller than a single alphanumeric character, such as individual sample points or equal-length (in time or space) collections of sequential sample points. Although local features are more sensitive to handwriting variations than are global features, they also tend to require more computer resources for processing and storage. Therefore, an appropriate feature set often includes a combination of global and local features, chosen for an advantageous trade-off between discriminative power and compactness.
A given pair of signatures by the same person seldom coincides completely. More typically, the signatures differ in such a way that small, localized elongations or compressions are needed to bring into registry the segments on which corresponding local features are computed. Therefore, it is often desirable, when comparing local features, to employ a technique in which the comparison is made elastically. One such technique is Dynamic Warping, as described, for example, in Y. Sato et al., "Online Signature Verification Based on Shape, Motion, and Writing," in Proc. 6.sup.th of ICPR (1982) 823-826 (IEEE Publication No. CH 1801-0/82/0000/0823).
Another comparison technique, which also has the inherent ability to deal with differences of this kind, uses Hidden Markov Modeling (HMM). HMM is described generally, and with reference to applications for speech recognition, in L. R. Rabiner, "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition," Proc. of the IEEE 77 (February 1989) 257-284. An application of HMM to signature verification is described in L. Yang et al., "Application of Hidden Markov Models for Signature Verification," Pattern Recognition 28 (1995) 161-170.
Briefly, the signature is characterized by a sequence of observables. For signatures of each class (i.e., signatures by each registered human subject), a respective hidden Markov model is posited to underlie the signing process. This model consists of a finite sequence of states. Associated with each state is a probability distribution for observations generated in that state. Also associated with each state (except the last) is a probability of transition into the next state in the next time step. In the method of Yang et al., a self-transition probability is also associated with each state. The hidden Markov model is constructed from a set of reference signatures.
For any given signature, the signing process must pass through all of the states. However, the number of observables is generally much greater than the number of states. Therefore, at least some of the states will endure for more than one time step, and thus will experience at least one self-transition. This variability in the state duration provides the flexibility, referred to above, for dealing with variations between signatures by the same person.
A given signature is verified by calculating the probability that it was generated by the hidden Markov model of its purported class. This probability depends on the transition probabilities and on the state-specific observation-probability distributions. If the calculated probability satisfies a threshold test, the signature is deemed authentic.
An ideal signature verification method is capable of perfect discrimination between genuine signatures and forgeries. That is, the rate of false acceptances (of forged signatures) and the rate of false rejections (of genuine signatures) are ideally both zero. However, because of human variability in making signatures, it is rare to find a criterion that discriminates perfectly, in all cases, between those signatures that are genuine and those that are forged. Therefore, in practice, a moderate rate of errors of both types must generally be tolerated.
Better understanding of human behavior and kinesiology in the writing of signatures can lead to better modeling of the signing process and, in turn, to greater accuracy in signature verification.
In particular, there is room to improve HMM methods, as they are currently known, by more closely modeling certain behavioral peculiarities of the signing process.